Facing an unassailable 3-0 deficit going into the final game of the series, the Black Caps reduced their opponents to 123 for eight from 28.3 overs despite a defiant 60 from opener Upul Tharanga.
But the rain which affected the World Twenty20 in the same country has decimated this tour, washing out the one-off T20 clash and the first ODI and restricting play in the others, and returned in earnest to prevent the tourists seizing on their advantage.
Tim Southee took three for 18 and gave his side a great start when he bowled Dinesh Chandimal in the second over and also accounted for Lahiru Thirimanne (17), who edged a wide delivery to wicketkeeper BJ Watling.
Angelo Mathews failed to trouble the scorers and Kumar Sangakkara made just five before becoming Adam Milne's first victim in ODIs but Tharanga finally found support from Mahela Jayawardene.
The pair put on 47 before Jayawardene (24) took a sharp single to cover but was run out by Nathan McCullum's superb throw on the turn.
Jeevan Mendis followed later in the same Andrew Ellis over for a duck but Tharanga reached an 88-ball half-century with two boundaries in Ellis' next over.
Thisara Perera fell for 11 and Tharanga edged the returning Southee to Watling to end his 94-ball vigil just as the rain started to fall. With no let-up, play was eventually called off around three hours and 45 minutes later.